The usual Auto regressive process considers the time t from negative infinity and positive infinity, but what if we restrict our time to strict positive space, do we still have our stationary result?
For example, let {$e_{t}$} be a sequence of i.i.d random variables, t= 1, 2, 3... If $|\rho| < 1$, then the consider the sequence $$y_{t+1} = \rho y_{t} + e_{t+1}$$ If $y_{0}$ is a random variable, is the sequence {$y_{t}$}, t > 0 strictly stationary?
Any help is extremely appreciated